# st: Re: st: RE: how to test with two suspect endogenous variables？

 From gjhxmu@sina.com To statalist Subject st: Re: st: RE: how to test with two suspect endogenous variables？ Date Tue, 26 May 2009 20:21:43 +0800

```Dear Mark,

Thank you very much! I learn a lot from what you replied.

Maybe my expression is implicit. I am sorry. I expound below.

My equation is

y=al+a2x1+a3x2+a4z+e
where z is exogenous definitely.However, I suspect whether x1 or x2 or both are endogenous.
there are two instrument variables, z1 for x1 and z2 for x2.

I can test whether x1 and x2 are both endogenous, using -ivreg2- in which I put both in the-endog()- option varlist. i.e, Ho is x1 is exog AND x2 is exog. If the p value is not significant, I can conclude both are exdogenous.However, if the p value is significant, at least one variable is endogenous.

Then I just want to check which one or both is endogenous. I do not know how to do that, especially how to treat the other suspect endogenous variable when testing one suspect endogenous varible.Treat it exogenous or endogenous?

Take testing x1 for example, following wooldridge I first regress x1 on all exogenous variables to get residual. If I treat x2 as exogenous, all exgenous variables include z , z1 and x2; If I treat x2 as endogenous, all exogenous variables include z, z1 and z2. Obviously, the "treating mode" makes results different.

In a word, how to check which variable or both is endogenous after rejecting the null hypothesis that both are exogenous?

Hope my expression is better now. Please forgive me if anything wrong is expressed.

Best wishes,

Rose.

----- Original Message -----
From: Schaffer, Mark E <M.E.Schaffer@hw.ac.uk>
To: <statalist@hsphsun2.harvard.edu>
Subject: st: RE: how to test with two suspect endogenous variables？
Date: 2009-5-24 22:13:17

Rose,

A few points to make here:

- First, you are working with a single equation ("limited information estimation"), not a system of equations. In this context, you can't really say "z1 is the IV for x1" and "z2 is the IV for x2". The IV estimator uses both (if you did the estimation by hand using 2SLS, you'd take your linear projections in the first stage using BOTH z1 and z2). There are some good past Statalist posts on this by Kit Baum that you might want to look up.

- Second, you probably don't want to us classical Durbin-Wu-Hausman. If you use a GMM distance test ("difference-in-Sargan", "C-test"), you can get robustness to heteroskedasticity, serial correlation, whatever. DWH will be a special case. -ivreg2- has this facility with the -endog- and -orthog- options.

- Third, it sounds like the natural null hypothesis for you is Ho: x1 is exog AND x2 is exog. You'd reject this if either x1 or x2 is endog. You can test this in -ivreg2- by estimating your equation with x1 and x2 as exogenous, an empty endogenous variable list, z1 and z2 as exogenous instruments, and x1 and x2 in the -orthog()- option variable list. This compares the specification with x1/x2 as exogenous vs. the specification with them as endogenous. Alternatively, you can estimate the equation with x1/x2 as endogenous and instrumented with z1/z2, and test whether you can treat them as exogenous by putting them in the -endog()- option varlist.

- Fourth, you need to believe that your IVs meet the requirements of orthogonality and relevance. Orthogonality won't be testable in this case because the eqn is exactly identified, but you can and should test their relevance (Cragg-Donald, Anderson, Kleibergen-Paap, et al.) in the specification with x1/x2 as exogenous.

The -ivreg2- options and the theory behind them are discussed in the Baum-Schaffer-Stillman 2003 and 2007 Stata Journal articles.

Hope this helps.

Best wishes,
Mark

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
> gjhxmu@sina.com
> Sent: 23 May 2009 18:42
> To: statalist
> Subject: st: how to test with two suspect endogenous variables？
>
> Dear all,
> I encountered a problem with endogeniety.Concretely, I have a
> equation below:
> y=al+a2x1+a3x2+a4z+e
> where z is exogenous definitely.However, I suspect whether x1
> and x2 are endogenous.
> and there are two instrument variables, z1 for x1 and z2 for x2.
>
> In wooldridge book, there is an introduction about how to
> test whether one variable is endogenous.i.e,hausman test.
> First get the residual and then add the residual to the
> equation.If the p value of residual is significant, the
> suspect variable is endogenous.
>
> However, how to test with two suspect endogenous variables?
>
> Hope replies sincerely. Thank you in advance.
>
> Rose
>
> *
> * For searches and help try:
> * http://www.stata.com/help.cgi?search
> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
>

--
Heriot-Watt University is a Scottish charity
registered under charity number SC000278.

*
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```